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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.ode.nonstiff;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    /**<a name="line.21"></a>
<FONT color="green">022</FONT>     * This class implements the 5(4) Dormand-Prince integrator for Ordinary<a name="line.22"></a>
<FONT color="green">023</FONT>     * Differential Equations.<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>     * &lt;p&gt;This integrator is an embedded Runge-Kutta integrator<a name="line.25"></a>
<FONT color="green">026</FONT>     * of order 5(4) used in local extrapolation mode (i.e. the solution<a name="line.26"></a>
<FONT color="green">027</FONT>     * is computed using the high order formula) with stepsize control<a name="line.27"></a>
<FONT color="green">028</FONT>     * (and automatic step initialization) and continuous output. This<a name="line.28"></a>
<FONT color="green">029</FONT>     * method uses 7 functions evaluations per step. However, since this<a name="line.29"></a>
<FONT color="green">030</FONT>     * is an &lt;i&gt;fsal&lt;/i&gt;, the last evaluation of one step is the same as<a name="line.30"></a>
<FONT color="green">031</FONT>     * the first evaluation of the next step and hence can be avoided. So<a name="line.31"></a>
<FONT color="green">032</FONT>     * the cost is really 6 functions evaluations per step.&lt;/p&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;p&gt;This method has been published (whithout the continuous output<a name="line.34"></a>
<FONT color="green">035</FONT>     * that was added by Shampine in 1986) in the following article :<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;pre&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     *  A family of embedded Runge-Kutta formulae<a name="line.37"></a>
<FONT color="green">038</FONT>     *  J. R. Dormand and P. J. Prince<a name="line.38"></a>
<FONT color="green">039</FONT>     *  Journal of Computational and Applied Mathematics<a name="line.39"></a>
<FONT color="green">040</FONT>     *  volume 6, no 1, 1980, pp. 19-26<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;/pre&gt;&lt;/p&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     *<a name="line.42"></a>
<FONT color="green">043</FONT>     * @version $Revision: 786881 $ $Date: 2009-06-20 14:53:08 -0400 (Sat, 20 Jun 2009) $<a name="line.43"></a>
<FONT color="green">044</FONT>     * @since 1.2<a name="line.44"></a>
<FONT color="green">045</FONT>     */<a name="line.45"></a>
<FONT color="green">046</FONT>    <a name="line.46"></a>
<FONT color="green">047</FONT>    public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>      /** Integrator method name. */<a name="line.49"></a>
<FONT color="green">050</FONT>      private static final String METHOD_NAME = "Dormand-Prince 5(4)";<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>      /** Time steps Butcher array. */<a name="line.52"></a>
<FONT color="green">053</FONT>      private static final double[] staticC = {<a name="line.53"></a>
<FONT color="green">054</FONT>        1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0<a name="line.54"></a>
<FONT color="green">055</FONT>      };<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>      /** Internal weights Butcher array. */<a name="line.57"></a>
<FONT color="green">058</FONT>      private static final double[][] staticA = {<a name="line.58"></a>
<FONT color="green">059</FONT>        {1.0/5.0},<a name="line.59"></a>
<FONT color="green">060</FONT>        {3.0/40.0, 9.0/40.0},<a name="line.60"></a>
<FONT color="green">061</FONT>        {44.0/45.0, -56.0/15.0, 32.0/9.0},<a name="line.61"></a>
<FONT color="green">062</FONT>        {19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0,  -212.0/729.0},<a name="line.62"></a>
<FONT color="green">063</FONT>        {9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0},<a name="line.63"></a>
<FONT color="green">064</FONT>        {35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0}<a name="line.64"></a>
<FONT color="green">065</FONT>      };<a name="line.65"></a>
<FONT color="green">066</FONT>    <a name="line.66"></a>
<FONT color="green">067</FONT>      /** Propagation weights Butcher array. */<a name="line.67"></a>
<FONT color="green">068</FONT>      private static final double[] staticB = {<a name="line.68"></a>
<FONT color="green">069</FONT>        35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0<a name="line.69"></a>
<FONT color="green">070</FONT>      };<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>      /** Error array, element 1. */<a name="line.72"></a>
<FONT color="green">073</FONT>      private static final double e1 =     71.0 / 57600.0;<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>      // element 2 is zero, so it is neither stored nor used<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>      /** Error array, element 3. */<a name="line.77"></a>
<FONT color="green">078</FONT>      private static final double e3 =    -71.0 / 16695.0;<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>      /** Error array, element 4. */<a name="line.80"></a>
<FONT color="green">081</FONT>      private static final double e4 =     71.0 / 1920.0;<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>      /** Error array, element 5. */<a name="line.83"></a>
<FONT color="green">084</FONT>      private static final double e5 = -17253.0 / 339200.0;<a name="line.84"></a>
<FONT color="green">085</FONT>    <a name="line.85"></a>
<FONT color="green">086</FONT>      /** Error array, element 6. */<a name="line.86"></a>
<FONT color="green">087</FONT>      private static final double e6 =     22.0 / 525.0;<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>      /** Error array, element 7. */<a name="line.89"></a>
<FONT color="green">090</FONT>      private static final double e7 =     -1.0 / 40.0;<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>      /** Simple constructor.<a name="line.92"></a>
<FONT color="green">093</FONT>       * Build a fifth order Dormand-Prince integrator with the given step bounds<a name="line.93"></a>
<FONT color="green">094</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.94"></a>
<FONT color="green">095</FONT>       * integration), the last step can be smaller than this<a name="line.95"></a>
<FONT color="green">096</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.96"></a>
<FONT color="green">097</FONT>       * integration)<a name="line.97"></a>
<FONT color="green">098</FONT>       * @param scalAbsoluteTolerance allowed absolute error<a name="line.98"></a>
<FONT color="green">099</FONT>       * @param scalRelativeTolerance allowed relative error<a name="line.99"></a>
<FONT color="green">100</FONT>       */<a name="line.100"></a>
<FONT color="green">101</FONT>      public DormandPrince54Integrator(final double minStep, final double maxStep,<a name="line.101"></a>
<FONT color="green">102</FONT>                                       final double scalAbsoluteTolerance,<a name="line.102"></a>
<FONT color="green">103</FONT>                                       final double scalRelativeTolerance) {<a name="line.103"></a>
<FONT color="green">104</FONT>        super(METHOD_NAME, true, staticC, staticA, staticB, new DormandPrince54StepInterpolator(),<a name="line.104"></a>
<FONT color="green">105</FONT>              minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.105"></a>
<FONT color="green">106</FONT>      }<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>      /** Simple constructor.<a name="line.108"></a>
<FONT color="green">109</FONT>       * Build a fifth order Dormand-Prince integrator with the given step bounds<a name="line.109"></a>
<FONT color="green">110</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.110"></a>
<FONT color="green">111</FONT>       * integration), the last step can be smaller than this<a name="line.111"></a>
<FONT color="green">112</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.112"></a>
<FONT color="green">113</FONT>       * integration)<a name="line.113"></a>
<FONT color="green">114</FONT>       * @param vecAbsoluteTolerance allowed absolute error<a name="line.114"></a>
<FONT color="green">115</FONT>       * @param vecRelativeTolerance allowed relative error<a name="line.115"></a>
<FONT color="green">116</FONT>       */<a name="line.116"></a>
<FONT color="green">117</FONT>      public DormandPrince54Integrator(final double minStep, final double maxStep,<a name="line.117"></a>
<FONT color="green">118</FONT>                                       final double[] vecAbsoluteTolerance,<a name="line.118"></a>
<FONT color="green">119</FONT>                                       final double[] vecRelativeTolerance) {<a name="line.119"></a>
<FONT color="green">120</FONT>        super(METHOD_NAME, true, staticC, staticA, staticB, new DormandPrince54StepInterpolator(),<a name="line.120"></a>
<FONT color="green">121</FONT>              minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.121"></a>
<FONT color="green">122</FONT>      }<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>      /** {@inheritDoc} */<a name="line.124"></a>
<FONT color="green">125</FONT>      @Override<a name="line.125"></a>
<FONT color="green">126</FONT>      public int getOrder() {<a name="line.126"></a>
<FONT color="green">127</FONT>        return 5;<a name="line.127"></a>
<FONT color="green">128</FONT>      }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>      /** {@inheritDoc} */<a name="line.130"></a>
<FONT color="green">131</FONT>      @Override<a name="line.131"></a>
<FONT color="green">132</FONT>      protected double estimateError(final double[][] yDotK,<a name="line.132"></a>
<FONT color="green">133</FONT>                                     final double[] y0, final double[] y1,<a name="line.133"></a>
<FONT color="green">134</FONT>                                     final double h) {<a name="line.134"></a>
<FONT color="green">135</FONT>    <a name="line.135"></a>
<FONT color="green">136</FONT>        double error = 0;<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>        for (int j = 0; j &lt; y0.length; ++j) {<a name="line.138"></a>
<FONT color="green">139</FONT>            final double errSum = e1 * yDotK[0][j] +  e3 * yDotK[2][j] +<a name="line.139"></a>
<FONT color="green">140</FONT>                                  e4 * yDotK[3][j] +  e5 * yDotK[4][j] +<a name="line.140"></a>
<FONT color="green">141</FONT>                                  e6 * yDotK[5][j] +  e7 * yDotK[6][j];<a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>            final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));<a name="line.143"></a>
<FONT color="green">144</FONT>            final double tol = (vecAbsoluteTolerance == null) ?<a name="line.144"></a>
<FONT color="green">145</FONT>                               (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :<a name="line.145"></a>
<FONT color="green">146</FONT>                                   (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);<a name="line.146"></a>
<FONT color="green">147</FONT>            final double ratio  = h * errSum / tol;<a name="line.147"></a>
<FONT color="green">148</FONT>            error += ratio * ratio;<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>        }<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>        return Math.sqrt(error / y0.length);<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>      }<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>    }<a name="line.156"></a>




























































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